Logarithmic-tail Fréchet normalization
= Logarithmic-tail Fréchet normalization
{title2=$a_n\log a_n=n$}
For a <distribution function> with tail $1-F(x)=1/(x\log x)$, let $a_n>1$ solve $a_n\log a_n=n$. Then $n(1-F(a_nx))\to1/x$ for $x>0$, so the normalized <sample maximum> tends to the shape-one <Fréchet distribution>. The inequalities $n/\log n<a_n<n/(\log n-\log\log n)$ for large $n$ show $a_n\sim n/\log n$, allowing that simpler scale too.